The generalized Chazy equation and Schwarzian triangle functions (Q1585466)

While considering an integrable third-order system of Darboux-Halphen type that depends on three arbitrary parameters \(\alpha\), \(\beta\) and \(\gamma\), the authors give the general solution to the system in terms of Schwarzian triangle functions associated with circular triangles with angles \(\alpha\pi\), \(\beta\pi\) and \(\gamma\pi\). The authors show that for special choices of the parameters the Darboux-Halphen system reduces to the generalized Chazy equation.